How can I write an essay on "The Lion and the Boar" by Aesop?

The hot desert sun blares down upon the inhabitants. Some will fight for the little water and some will wait and seize the opportunities when it arrives. Which one would work best for you? Will you be one to fight for your needs or wait for your needs to be met? Would you work to find a resolution so everyone gets a little of what they need? If a resolution is not reached those who argue are often watched by others who will take advantage of their defeat to benefit themselves. These are the important messages that can be found in The Lion and The Boar which is one of Aesop's Fables.
Aesop’s Fables are a collection of words written by Aesop in ancient Greece. These fables were passed on orally to teach morals to those who hear them. In the case of The Lion and The Boar, Aesop was teaching listeners that in conflicts there are those who argue, those who compromise, those who take advantage of the situation, and those who wait and go without. This holds true today as well as in ancient Greece.
The lion, known as the king, is arguing with the boar, also another animal known for strength. They are arguing for the one thing they both want, water. While they are busy arguing, the vultures watch with care and are waiting for the opportunity to benefit from their fighting. When one of the animals falls, the vultures will have food to survive. The boar and the lion realize the vultures plan and they decide to work together to share the water which leaves the vultures without food. Many things can be said about this fable.
We live in a world of conflict and war. In war, there are no winners, someone is always left without as the vultures were in this story. It also touches on the fact that compromise can be useful in conflict resolution where both parties get a little of what they want, but not the entire of what they want. It is important to know all sides of conflict so that the best decision can be made at the time. If we let our greed and wants take over our needs, we most likely will lose in the end. If we are in waiting, as were the vultures and a benefit does not come of watching the conflict, you may go without all together. Aesop may have been making a motion for self reliance and perseverance, compromise, and seize the opportunity in one short fable.

You don't say what kind of essay you need to write, or how long it should be, but I will give you some suggestions as to what you could talk about and key points to cover.
This is an extremely short fable about a lion and a boar who come to a drinking hole at the same time, on a day when the heat has driven all the animals to try and seek out water. As such, when the lion and the boar, both symbolically strong animals, reach the water, they begin to fight with each other over which of them should get to drink. When they pause for breath, however, they see a group of vultures waiting in the distance and realize that the vultures have gathered in anticipation of either the lion or the boar being killed in the fight. Whichever is killed will be eaten by the vultures.
When they realize this, the lion and the boar decide to simply drink together as friends, because this is far preferable than either one of them becoming the vultures' food.
In your essay, you may wish to create a thesis based on what you think the moral of this story is. The moral is usually interpreted as something like: when two people fight, there is often someone waiting in the wings to take advantage of their defeat.
In writing your essay, then, you might consider how this story is applicable to the modern day. What is it really saying?
It is interesting that the two animals who are fighting are a lion and a boar. Both the lion and the boar are symbols of great strength, but the point of the story seems to be that if one great strength cancels out another, the one that remains will end up in a weakened position. Through fighting unnecessarily, it diminishes its own strength, allowing others to prey upon it.
You could argue as to who or what the vultures might represent. A vulture is a creature that waits until an animal is dead to feast upon its corpse; it does not get involved in fights itself, but simply waits until others have destroyed themselves. In the modern day, tabloid journalists are often referred to as "vultures," who wait for events to happen and then "prey" on the aftermath for their writing. The term "vulture" usually indicates that somebody is extremely unscrupulous and without morals. In adapting the context of this story, then, if we see the vultures as predatory journalists, who could the lion and the boar represent? They could be two high-level celebrities having a public argument, after which the vultures of the press will destroy the reputation of the losing one. Or we could interpret the lion and the boar as two great powers at war, with the vultures being a weaker country who waits until the fight has diminished the two big armies in order to creep in and claim victory, one country now being defeated and the other greatly weakened.
There are lots of essays you could write about this story, but because it is so brief, I think a good angle to take would be to summarize the story, explain the moral, and then argue that the moral is still applicable to us today. You could then identify several situations in which the story could be applicable, and explain what it would mean in those contexts. I hope the above suggestions give you a place to start.